Indirect Searches for Dark Matter
Tau Neutrino Physics: An Introduction
Barry C. Barish
California Institute of Technology
Pasadena, CA 91125, U.S.A.
The properties of the tau neutrino are discussed and the recent result reporting direct detection for the first time is presented. The status of the experimental results relating to the mass of the , both from missing energy in tau decays and from neutrino oscillation experiments are reviewed. Finally, I give a perspective on future directions in studies of the physics of tau neutrinos.
1. INTRODUCTION
The tau neutrino was inferred as the third neutrino (e, and ) at the time the tau lepton was discovered and determined to be a lepton. Since that time, direct studies of the have proven elusive, however, due to the fact that the tau is so heavy and difficult to abundantly produce. Finally, the fact that the tau is very short lived makes the creation of an intense ‘beam’ of tau neutrinos not so simple.
Much is known about the properties of the tau neutrino despite the fact that direct detection has only been reported this past summer. In fact, that detection is clearly one of the more important results experimental results reported in high energy physics this year. I review that evidence in this presentation and a more complete talk will be given later in this workshop.
It is interesting that the was the last of the leptons and quarks in the three families to be observed in the laboratory, even after the top quark, which took a huge effort at Fermilab to pin down and measure the mass. The fact that the is the last to be detected is an indication of the experimental challenge that was involved in making the direct detection of interactions.
The main interest in the has focused on the issue of neutrino mass and oscillations. Direct mass measurements have yielded limits on the neutrino mass, while the indications are very strong that atmospheric neutrino observations indicated oscillations between the muon neutrino and the tau neutrino with a mass difference of m2 ~ 10-3 eV2. This, of course, implies that the has finite mass, but undoubtedly much smaller than the limits set in the direct mass measurements.
Future developments in tau neutrino physics look quite promising. Experiments observing supernovae could lead to quite accurate mass determinations, tau neutrinos might play an important role in the interpretation of the observations of high energy cosmic rays above the Greisen, Kuzmin, Zatsepin (GKZ) bound indicating new physics.
Finally long baseline neutrino experiments will be able to study the role of the tau neutrino in the atmospheric neutrino oscillations with precision, with the possibility of an even more powerful experimental probe in the future if a neutrino factory is built, offering perhaps even the possibility of observing CP violation in the neutrino sector.
2. THE NUMBER OF NEUTRINOS
The evidence that there are three families of quarks and leptons is strong. Of course we are left with the puzzle why there are the three families, as well as the problem of determining the large mass splittings between the families. The evidence for the number of standard neutrinos comes from two sources: big bang nucleosynthesis, and the accurate determination that comes from the partial widths in Z-decay measured at LEP.
2.1. Big Bang Nucleosynthesis
The earlies indications that there are a finite and small number of families in nature came from big bang nucleosynthesis.
The primordial abundances determined for D, 3He, 4He and 7Li are affected by the number of neutrinos produced in the big bang. The predictions and understanding of these abudndances[1] is a major triumph of the standard big bang model of the early universe. The abundances of these light elements range over nine orders of magnitude! The first constraint on these abundances is on Y, the 4He fraction. From number of neutrons when nucleosynthesis began, we know that Y is bounded, Y < 0.25.
Figure 1. The abundances of light elements in nucleosynthesis, which vary by a factor of 109 are shown. The parameter is the baryon to photon ratio x1010, which is not well determined.
The observed value of Y (figure 1) is
Yobserved = 0.238±0.002±0.005
The presence of additional neutrinos would at the time of nucleosynthesis increases the energy density of the Universe and hence the expansion rate, leading to larger Y. The relation below gives the magnitude of the effect due to an additional neutrino,
YBBN= 0.012-0.014 N
The result of an analysis of the results in figure 1, as a function of h and DYBBN gives a bound of the number of light neutrinos
n
Although this limit is not nearly as good as has been obtained from LEP eeresults, it is a quite independent method.
2.2 Number of Neutrinos from LEP data
The most precise measurements of the number of light neutrinos come from Z → e+ + e- partial width measurements at LEP. The invisible partial width, Ginv, is determined by subtracting the measured visible partial widths (Z decays to quarks and charged leptons) from the Z width. The invisible width is assumed to be due to N
In the Standard Model, (/l)SM = 1.991 ± 0.001,where using the ratio reduces the model dependence. Using this prediction and comparing with the accurate LEP measurements, the value [5] for the number of neutrinos is bounded by
N = 2.984 ±0.008
This impressive measurement gives strong credence to the view that there are three families of leptons and quarks
3. TAU NEUTRINO EXISTENCE
The existence of the tau neutrino has relied on the indirect (though very strong) evidence until this past summer. The initial evidence was presented by Feldman et al [6] in 1981 from tau decay data. The DONUT experiment [7] at Fermilab has now reported the first direct observations of detected interactions. They observe the tau and its decays from charged current interactions
The general principal of the DONUT experiment is to produce a strong source of tau neutrinos by interactions of the 800 GeV proton beam with a beam dump. The proton interactions produce a large number of Ds, having a very short lifetime and subsequently yielding ’s in the final state. This scheme to produce the intense beam of tau neutrinos is shown in figure 2. The data run reported used an integrated total number of protons on target of 3.6 1017 , and the data was taken from April to September 1997.
Figure 2. The DONUT tau neutrino beam is created using 800 GeV protons incident on a beam dump as shown.
The beam then passes through a thick shielding of material and magnetic field and enters into the magnetic spectrometer of the detector. The actual detector for analyzing events was made from a sandwich of layers of emulsion detectors giving the required spatial resolution to reconstruct tau decays (eg. the produced tau frominteractions goes only about 1 mm in space before decaying. This vertex detector also has active scintillating fiber detectors, which help pick event candidates from background. The larger spectrometer consists of magnet, drift chambers, calorimeters and muon detectors all used to trigger the device and find the rare tau neutrino events with good efficiency.
Figure 2. A source of tau neutrinos for the DONUT experiment are Ds decays from 800 GeV interactions in the beam dump.
The total he expected number of interactions is estimated to be ~1100 ( , e , ) for the entire DONUT data run. They found 203 candidates for in a total of 6.6 106 triggers. The reported events satisfied the event topology shown in figure 3, where they measure the parent tau and identify a kink . They also search for the topology were the tau is too short lived to emerge from the 1 mm steel absorber, but they have not reported on that topology. In that case, they do not measure the parent tau but identify the candidates by the apparent kink when the track is projected back toward the vertex.
Figure 3. The event topology signature for observing tau neutrino interactions in the DONUT experiment. The parent tau is indentified and the kink from the subsequent tau decay is observed and measured using nuclear emultions.
The final experimental challenge is ‘proving’ that the observed events are due to tau neutrino interactions and not background events satisfying the topological requirements. Detailed tests and modeling has been done to understand the backgrounds, as well as characterizing measured parameters that can at least statistically distinguish tau neutrino events from background. Background events can come from various sources like overlapping events (randomly associated tracks) that fake this topology, scattering of a track to look like a kink or reconstructed charm events D+ decays without the lepton identified. Fig. 4 illustrates the pT distribution of both ‘signal’ events and the candidates identified as background events. As a result of a detailed analsysis of the candidate events, their final result is summarized below.
events observed 4
expected 4.1 ± 1.4 background
0.41± 0.15
There are background sources that can satisfy this topology. The primary backgrounds include randomly associated extra tracks giving an apparent kink, interactions of outgoing particles giving an apparent kink and charm background (Ds decay). They have both estimated these backgrounds and performed various tests that distinguish the signal. The result
Figure 4. The pT distribution of candidate events, where the events identified as events typically have larger pT.
4. Tau Neutrino Properties
4.1 Spin of the
The spin of the has been established [5] as J = 1/2. The possibility of J = 3/2 has been ruled out by establishing that the - is not in a pure H ± -1 helicity state in the decay
4.2 Magnetic Moment of
We expect
mn = 0 for Majorana or chiral massless Dirac neutrinos. If
SU(2)xU(1) is extended to include massive neutrinos,
where m is in eV and B = eh/2me Bohr magnetons. Using the upper bound m < 18 MeV, one obtains m < 0.6 10-11 mB. This should be compared to the experimental limit of m < 5.4 10-7 mB from + e- + e- scattering as measured in BEBC.
4.3 Electric Dipole Moment of the
The electric dipole moment of the has been established as < 5.2 10-17 e cm from (Z ee) at LEP.
4.4 Charge
The charge of the nt has been determined to be < 2 10-14 from the Luminosity of Red Giants [8]
4.5 Lifetime
The lifetime has been determined to be > 2.8 1015 sec/eV Astrophysics for m < 50 eV
[9]
4.6 Direct Mass Measurement of
Direct bounds on the mass come from reconstruction of multi-hadronic decays. The best limits come from the Aleph experiment at LEP studying the reactions [10]:
-+
they set a limit of m < 22.3 MeV from a total of 2939 events.
--+0
they set a limit of m < 21.5 MeV/c2 from 52 events.
The combined limit is
m < 18.2 MeV/c2
The method is to analyze event topologies having very little Q-value phenomenologically as two body
decays
-ph- Ehphp
In the
tau rest frame, the hadronic energy is
hm+mh2 +m2) / 2m
In the
laboratory frame
Eh = (Eh* + ph* cos)
interval bounded for different m
Ehmax,min = (Eh* ± ph*)
Figure 5 illustrates two sample events superposed on the kinematical limits for different neutrino masses illustrating how the events limit the neutrino mass.
Figure 5. Two sample events from the reaction --+0 with the error contours to be compared with the kinematic limits for different neutrino masses.
Figure 6. The reconstructed events from Aleph for the reaction displayed on top of the kinematical limits for m = 0 (shaded) and m = 23 MeV (line).
The likelihood fit for all the events from the reaction is shown in Fig 7 yielding a 90% confidence limit of ~ 23 MeV.
Figure 7. The log likelihood fit for the tau neutrino mass using the method and data described above for the Aleph experiment at CERN using the reaction
5. Neutrino Oscillations
5.1 Introduction to Neutrino Oscillations
Neutrino oscillations were first suggested by B. Pontecorvo in 1957 after the discovery of oscillations in the kaon sector. If neutrinos have mass, then a neutrino of definite flavor, , is not necessarily a mass eigenstate. In analogy to the quark sector the could be a coherent superposition of mass eigenstates.
The fact that a neutrino of definite flavor is a superposition of several mass eigenstates, whose differing masses Mm cause them to propagate differently, leads to neutrino oscillations: the transformation in vacuum of a neutrino of one flavor into one of a different flavor as the neutrino moves through empty space. The amplitude for the transformation l l’ is given by:
where U is a 3 x 3 unitary matrix in the hypothesis of the 3 standard neutrino flavors (e). In the hypothesis of a sterile neutrino U is a 4 x 4 unitary matrix.
The probability P(l l’ ) for a neutrino of flavor l to oscillate in vacuum into one of flavor l’ is then just the square of this amplitude. For two neutrino oscillations and in vacuum:
Where M2 is in eV2, L in km and E in GeV. Figure 8 shows the oscillation phenomena as a function of the parameter L/E. The example chosen is for m2 = 3 10-3 eV2, which is the nominal value for the neutrino osciallation solutions to the atmospheric neutrino data described below. Note that the probability is P = ½ for large values of L/E and the most sensitive regime to see the effect of neutrino oscillations is when L/E ~ 1/m2. These parameters are important in the discussion of atmosheric neutrinos below, and the distance chosen for the next generation long baseline neutrino experiments.
Figure 8. Neutrino oscillation phenomena for various values of L/E using m2 = 3 10-3 eV2.
This simple relation should be modified when there is a difference in the interactions of the two neutrino flavors with matter. The neutrino weak potential in matter is:
where the upper sign refers to neutrinos, the lower sign to antineutrinos, GF is the Fermi constant, nB the baryon density, Yn the neutron and Ye the electron number per baryon (both about 1/2 in normal matter). Numerically we have
The weak potential in matter produces a phase shift that could modify the neutrino oscillation pattern if the oscillating neutrinos have differ ent interactions with matter. The matter effect could help to discriminate between different neutrino channels. According to the equation above the matter effect in the Earth could be important for e and for the s oscillations, while for oscillations there is no matter effect. For some particular values of the oscillation parameters the matter effect could enhance the oscillations originating "resonances" (MSW effect). The internal structure of the Earth could have an important role in the resonance pattern. However, for maximum mixing, the only possible effect is the reduction of the amplitude of oscillations.
Figure 9. Indications for neutrino oscillations from solar neutrinos , atmospheric neutrinos and from the LSND experiment at Los Alamos. The atmospheric neutrino favored solution is for the of indicating a mass difference of ~10-3 eV2 between the tau and muon neutrinos.
5.2 Atmospheric Neutrinos
There are several indications for neutrino oscillations, which are indicated in Fig. 9 [11]. However for the purpose of this presentation, which addresses the physics of the tau neutrino, the pertinent data is that on atmospheric neutrinos, which provide evidence for finite mass, and a mass difference between the tau neutrino and the muon neutrino of about 10-3 eV2. Below I review the status of the evidence in atmospheric neutrinos and the implications for the tau neutrino.
In the hadronic cascade produced from the primary cosmic ray we have the production of neutrinos with the following shower cascade:
P + Nucleus ’s + K’s + nucleons
(K) +
e + + e
From these decay channels one expects at low energies approximately twice as many muon neutrinos as electron neutrinos. Detailed corrections do not change this expectation appreciably. The calculation of the absolute neutrino fluxes is more difficult, with uncertainties due to the complicated shower de-
velopment in the atmosphere, uncertainties in the cosmic ray spectrum and to uncertainties in production cross sections.
The source of atmospheric neutrinos is from collisions at the top of the atmosphere of primary cosmic rays producing secondary pions and kaons. These secondary particles either subsequently interact producing a cascade of more pions and kaons or decay into muons and neutrinos. The decay products contain a muon neutrino and a muon. Finally, the muons themselves decay and producing both a muon and an electron neutrino.
The neutrinos are detected in large underground detectors measuring both the flux and the angular distribution. The difference in path length, L, giving sensitivity to neutrino oscillations is from L = 20 km for downward neutrinos near the zenith to L = 12700 km for those coming directly up through the earth near the zenith. Also, those coming up near the vertical go through the core of the earth and the effect can be enhanced by matter oscillations.
Figure 10. Atmospheric neutrinos produced in the atmosphere from high energy cosmic ray collisions near the top of the atmosphere. The zenith angle both allows sampling different distances for the neutrino to oscillate and upward neutrinos through the core of the earth can undergo matter oscillations described above.
There are two basic topologies of neutrino induced events in a detector: internally produced
events and externally produced events. The internally produced events have neutrino interaction vertices inside the detector. There are several hints for neutrino oscillations, which altogether make a strong case for finite neutrino mass.
Hint 1: Internal events, which are typically less than 1 GeV have been studied in many detectors. Due to the systematic difficulties mentioned above in accurately predicting the flux at these energies, the systematic errors are significantly reduced if the measured ratio of muon to electron neutrino events is measured, and in fact, usually the ratio of the ratios, R = (e)obs / (e)pred,
observed to predicted are given. The results are shown in Fig 11 and indicate fewer muon neutrinos than predicted from several experiments and, in particular, from the high statistics measurements. An obvious interpretation is that fewer muon neutrinos are observed because of neutrino oscillations causing some of the parent to ‘disappear’ because the neutrino has changed identity to another neutrino. As we will see, the most consistent interpretation is that the muon neutrino has oscillated into a tau neutrino.